This also applies to DDPMs.
Taking a recent DDPM model called Analytic-DDIM [1]} as an example, we calculate the corresponding frequency behavior function as shown in Figure REF (right).
On the contrary, this \(\kappa \)  is monotonically decreasing and \(\kappa <1\) , suggesting that Analytic-DDIM tends to shrink the high-frequency part of the output images.
This finding implies that NCSN++ and Analytic-DDIM may exhibit opposite behavior intrinsically.
According to [2]}, DDPMs and SGMs correspond to variance preserving (VP) and variance exploding (VE) stochastic different equation (SDE), respectively. Our above findings indicate that VE and VP SDEs might generally have opposite behaviors in the frequency domain in image generation.
This is inspiring for developing more proper SDEs to
better implement the diffusion process.
